How to move bone to the object position?
You should be able to:


Switch to object mode
Select the sphere
Object -> Snap -> Cursor to Selected
Select the bone/armature
Object -> Snap -> Selection to Cursor


This will move the entire armature so its origin is at the center of the sphere.

If you want to move the bone without affecting the armature origin (or if you have a multi-bone armature and only want to move one bone), then:


As above, set the cursor to the sphere's origin.
After selecting the armature, switch to edit mode and select the target bone.
If there are multiple bones in armature, make sure the target bone is disconnected (AltP -> Disconnect Bone)
Armature -> Snap -> Selection to Cursor